Relationship between compressive yield and tensile behavior in glassy thermoplastics

The effect of temperature and strain rate on the compressive yield behavior of polystyrene is compared with the effect of the same variables on crazing in tension. The results support the conclusion of other, more extensive work, which shows that crazing involves the same types of molecular processes as those which occur during deformation under compression and shear. An improved method of measuring compressive stress–strain curves is then described, and the compressive yield stress is also compared with an extrapolated tensile yield stress. The difference between the two is in line with concepts which assume a dependence of yield stress on the state of hydrostatic tension (or compression). It can be adequately described by the Mohr-Coulomb yield criterion. Application of this criterion also enables a theoretical stress strain curve in tension to be derived from other results in compression. Comparison of the tensile stress–strain curve so obtained with those which can be directly measured with other plastics, supports the hypothesis that crazing is favored by a marked decline in engineering stress during tensile elongation (plastic instability).     

Mechanical behavior of polymer microlayers

The mechanical behavior of polycarbonate (PC) coextruded as microlayers with a brittle polymer, either poly(styrene-co-acrylonitrile) (SAN) or poly(methyl methacrylate) (PMMA), was examined. Adhesion between layers was measured with the T-peel method. The much higher interfacial toughness of PC/PMMA microlayers compared to PC/SAN was attributed to partial miscibility. Comparison of the microdeformation behavior of 32-layer PC/SAN and PC/PMMA microlayers revealed that very good adhesion between PC and PMMA constrained yielding of the PC. This was seen in the tensile stress-strain curves as a broader stress drop at the yield point and a lower fracture strain. Decreasing the layer thickness by increasing the number of layers enhanced the ductility of both PC/SAN and PC/PMMA microlayers. A PC/PMMA microlayer with 4096 layers and a composition of 80% PC achieved the ballistic performance of polycarbonate.     

Rheology of PVC plastisol--VI: criteria for yielding and fracture of an immobilized layer

PVC plastisol exhibits pseudo-plastic flow in steady shear; that is, viscosity decreases with the increasing shear rate. At higher shear rates viscosity reaches a minimum and then increases, i.e., dilatant behavior. Previously, pseudo-plastic behavior was explained by a mechanism in which the suspended particles partition into an immobilized layer and a mobile phase. The development of the immobilized layer with the increase in shear rate was shown to quantitatively account for pseudo-plastic behavior. In higher shear rates dilatation of the immobilized layer was shown to be the cause of dilatacy. At even higher shear rates the immobilized layer fractures. In this paper the viscosity minimum was interpreted as the yielding of the immobilized layer. Subsequently, data in the literature were analyzed to find criteria for the yielding and fracture of the immobilized layer. Yielding was found to obey Coulomb's criterion, from which the coefficient of friction and the cohesive strength of the immobilized layer were evaluated. These properties were controlled by the nature of particle assembly in the immobilized layer and the plasticizer type had only a minor effect. The value of the coefficient of friction was on the lower side and within the range of values found in the literature for other materials. There were two modes of fracture of the immobilized layer, one with low strength, low strain to break, and the other with high strength, high strain to break. The former is analogous to the brittle fracture of solids and the latter ductile failure. The strength of brittle fracture was somewhat higher than cohesive strength, which was evaluated from yielding data. This is akin to Griffith's criterion for brittle fracture of a solid. Ductile failure occurred when the shear stress exceeded normal stress.     

Crazing in polyethylene

The tensile stress—strain curves of various types of polyethylene were compared from 77 to 298 K in nitrogen, isopentane, and the inert environment of helium at various strain rates. It was found that in general polyethylene crazes in a gas such as nitrogen at a temperature below 1.6 times its boiling point and in isopentane. Although the behavior of polyethylenes is similar to that of other polymers with regard to crazing in gases at low temperatures, they are in general less sensitive to the gas. The decrease in tensile strength of polyethylene in an environmental gas increases with crystallinity. The differences in the intrinsic low-temperature brittle fracture stress are attributed to differences in the density of tie molecules. The intrinsic yield point at room temperature showed the usual increase with increasing crystallinity, but all the polyethylenes have the same yield point below the γ transition temperature.     

Shear band formation and mode II fracture of polymeric glasses

Mode I and II fracture studies were performed from quasistatic to low velocity impact rates on polymethyl methacrylate (PMMA) and polycarbonate (PC). Mode II tests used an angled double‐edge notched specimen loaded in compression. The shear banding response of PMMA is shown to be highly sensitive to rate, with diffuse shear bands forming at low rates and sharp distinct shear bands forming at high rates. As the rate increases, shear deformation becomes more localized to the point where Mode II fracture occurs. PC is much less rate dependent and stable shear band propagation is observed over the range of rates studied with lesser amounts of localization. A new theory is formulated relating orientation in a shear band to intrinsic material properties obtained from true‐stress true‐strain tests. In a qualitative sense the theory predicts the high rate sensitivity of PMMA. A kinematic limit for orientation within a shear band is also derived based on entanglement network parameters. Mode II fracture in PMMA is shown to occur at this kinematic limit. For the case of PC, the maximum impact rates were not high enough to reach the kinematic limit. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

The effect of strain rate on solvent crazing of poly(ethylene terephthalate) in solutions of poly(ethylene oxide) of various molecular masses

The effect of strain rate on the behavior of PET during its tensile drawing in highly viscous liquids, such as liquid PEG (M 400) and semidilute solutions of PEO (M = (4 × 10⁴)−(1 × 10⁶)), is studied. With an increase in strain rate, the mechanism of tensile drawing of PET in PEG changes from solvent crazing to shearing; at the same time, over the selected interval of strain rates, tensile drawing of PET in semidilute solutions of PEO proceeds via the mechanism of solvent crazing. During tensile drawing of PET in PEO solutions, the behavior of PET is almost the same as the mechanism of tensile drawing in a pure solvent. This result indicates that, in the course of flow of the polymer solution through the formed porous structure, PEO is filtered off in the local tip region of the growing craze.     

Mechanical properties of glass continuous poly(cyclohexylethylene) block copolymers

The bulk mechanical properties of linear triblock and pentablock copolymers that self‐assemble into hexagonally packed cylinders with glassy, unentangled matrices of poly(cyclohexylethylene) (PCHE for a homopolymer, C for a block copolymer) with rubbery poly(ethylene‐alt‐propylene) (P) and semicrystalline polyethylene (E) minority components are examined. The tensile properties of high C content CEC triblock copolymer could not be quantified; however, CPC can plastically deform under uniaxial strain, unlike brittle PCHE. Both CECEC and CPCPC pentablock copolymers exhibited ductile tensile behavior, but the tensile properties of blends of these two pentablock copolymers show that the addition of crystallinity in the minority phase prevents strain softening after yielding and necking, which indicates that these samples deform only via crazing. On the other hand, the white gage region of CPCPC and the ability of CPCPC to neck indicate that high C content materials deform via shear yielding and crazing when the minority component is a rubbery material. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Quantitative approaches to particle cavitation,shear yielding,and crazing in rubber-toughened polymers

Models for rubber particle cavitation, shear yielding, and crazing are reviewed, and their ability to predict the large-strain deformation behavior of toughened polymers is discussed. An existing model for void initiation and expansion in rubber particles correctly predicts the observed trends: cavitation resistance increases when either the shear modulus or the surface energy of the rubber is increased, or the particle size is reduced. However, further work is needed to improve quantitative modeling of the thermally- and stress-activated void nucleation step. Shear yielding, which is also a rate process, is much better understood; here, the main problems in modeling relate to the formation and evolution of porous shear bands. Craze growth and failure are also reasonably well understood, but previous attempts at modeling have been hampered by uncertainties about craze initiation. To overcome these difficulties, a new theory of crazing is proposed, which treats initiation as a fracture process, and defines a new materials property, G_nasc, the energy required to form unit area of nascent craze. Because nascent crazes are ∼20 nm thick, G_nasc is low: calculations give values <0.5 J m⁻² for polystyrene. A new criterion incorporating a plasticity factor fits the data of Sternstein and coworkers on crazing under biaxial loading. In combination with theories of particle cavitation and shear yielding, the fracture mechanics model explains why the balance between crazing and shear yielding is governed by particle size, for example in ABS. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1399–1409, 2007     

A theory for environmental craze yielding of polymers at low temperatures

It has been recently discovered that polymers craze at low temperatures in the presence of nitrogen or argon. A quantitative theory has been developed which explains (1) the critical temperature above which the phenomenon disappears, (2) the critical stress for nucleating a craze, (3) the effect of strain rate on the yield point and size of crazes, (4) the drop in the load during craze yielding, and (5) the increase in strength of the polymer in N₂ or Ar at high strain rates so that the ultimate strength may exceed that in He or vacuum. The crazing action of the gases is described qualitatively at the molecular level.     

Mechanical properties and strain-rate effect of EVA/PMMA in situ polymerization blends

Transparent EVA/PMMA sheets are produced via in situ polymerization of MMA in this work. In the presence of the EVA-graft-PMMA (EVA-g-PMMA), which is synthesized by using tert-butyl peroctoate (t-BO) as initiator during MMA polymerization, EVA can be well dispersed in the PMMA matrix. Both tensile fracture energy and Izod impact strength of the EVA/PMMA blends are higher than those of the neat PMMA. SEM photos show that the grafted copolymer also prevents the dispersed EVA particles from being pulled out from the fracture surface. While the EVA/PMMA blends are investigated at room temperature over the strain rates of four decades (from 1.6 × 10⁻⁴ to 0.16 s⁻¹). It has an obvious transition, whereas the neat PMMA remains brittle over the entire range of strain rates.     

Mechanical behavior of polyester polymer concrete under low strain rate loading conditions

Polymer concrete (PC) has superior mechanical properties in comparison with cement concrete. In this research, the mechanical behavior of polyester polymer concrete (PPC) and its polyester resin were studied at different loading rates. Special specimens for testing the PPC and the polyester resin under low strain rate loading conditions were fabricated. Experiments were performed under different strain rates, from 0.00033 to 0.15 s⁻¹, and results for the PPC and the polyester resin were compared. Furthermore, the influence of strain rate on the mechanical response of the neat polyester and the PPC was investigated. The results show a maximum 40% increase in tensile strength of the neat polyester, while the elastic modulus does not change significantly. The compressive strength of the PPC increases by 25%. These results show that the mechanical behavior of the polyester resin and its PC is extremely sensitive to the strain rate.     

Morphology and toughness of coextruded PS/PMMA multilayers

The micromechanical behaviour of multilayered tapes made of two brittle incompatible amorphous polymers PS and PMMA was studied by means of an optical and a High Voltage Electron Microscope (HVEM). Microlayers of PS and PMMA were coextruded with varying number of layers: 64, 512 and 4096 layers. Mechanical properties of the PS/PMMA tapes were also examined. An increase in layer numbers was found to lead to a decrease in layer thickness that, in turn, resulted in: a) formation of thicker and longer crazes and, therefore, increased volume of the material involved in the plastic deformation; b) a noticeable increase in strength and strain at break (i.e. of toughness) of the samples. Enhanced toughness of the multilayered tapes is accounted for by massive cooperating crazing and yielding of both PS and PMMA phases.     

Adhesion through molecular entanglements in polymer interfaces

This paper examines the role of polymer interdiffusion or interpenetration along and across a boundary of two compatible but dissimilar polymers in controlling interfacial adhesion in the interface region (interphase). The effect of interphase adhesion on the mechanical properties as well as the deformation and fracture behavior of sandwich laminates of poly(methylmethacrylate) (PMMA) and poly(vinylidene) fluoride (PVF₂) have been studied. The interphase has been characterized using microscopy (optical, transmission, and scanning electron), dynamic mechanical spectroscopy, and x-ray microanalysis. Conditions of multiple crazing/fracture in the brittle phase (PMMA) and shear yielding in the ductile phase (PVF₂) are discussed. Scanning electron micrographs confirm these deformation modes in PMMA-PVF₂ sandwich composite laminates.     

The Mechanical Deformation Process of Electrospun Polymer Nanocomposite Fibers

Summary: The mechanical deformation processes of poly(methyl methacrylate)/ montmorillonite nanocomposites and their electrospun fibers were investigated by in situ tensile tests under a transmission electron microscope depending on their morphology. While the polymer nanocomposites deformed in a brittle manner, i.e., crazing, the electrospun polymer nanocomposite fibers deformed through a shear flow process leading to “nanonecking” due to the strong overlap of stress fields caused by nanopores within the fiber under a uniaxial tensile load. This unique change in deformation behavior provides the possibility that the intrinsic brittle material could be manipulated to be ductile without sacrificing its other attractive properties through a well‐controlled electrospinning process.

TEM micrograph of a low temperature fractured fiber showing the nanoporous surface structure.     

The ageing phenomenon of polyethersulphone hollow fibre membranes for gas separation and their characteristics

We have studied the ageing behaviour of PES/NMP (polyethersulphone/N-methyl pyrrolidone) hollow fibres for gas separation that were prepared from 35% and 37% dope. The effect of ageing on hollow fibres spun from low and high shear rate (103 vs. 862 s⁻¹) has also been investigated, in terms of their transport properties (permeation flux and separation performance), thermal, mechanical and tensile properties. Hollow fibres in this study were aged for around four months in ambient air at room temperature prior to testing.In general, the gas permeation flux drops steeply during the 40 days following fabrication and levels off thereafter. The O₂/N₂ selectivity decreases slightly over time. Hollow fibres spun with high shear rate seem to age faster than those spun with low shear rate. The gas fluxes of both membranes were found to follow a log–log relationship with ageing time. For almost all the gases used in this study, the gas flux decay rate, calculated from the slope of the log–log plot of gas flux vs. ageing, is higher for membranes spun with high shear rate. The effect of shear rate on ageing is less significant for smaller gas molecules that travel faster such as He and H₂. No significant effect of ageing on gas selectivity was observed. Experimental results also indicate that the storage modulus and loss modulus of the hollow fibres increase with ageing. Hollow fibres spun with high shear rates give a slightly higher increase in these moduli than those spun at low shear rates. Surprisingly, tangent δ (energy dissipation) and glass transitional temperature are not sensitive to ageing. We also found that the tensile yield strength and Young's modulus of the hollow fibres increase slightly with ageing. The hollow fibre membranes spun at high shear rates also show a higher increment in tensile yield stress. However, the change in Young's modulus due to ageing was similar for fibres spun with high and low shear rates.     

Rheological,mechanical and morphological properties of thermoplastic vulcanizates based on NR‐g‐PMMA/PMMA blends

Graft copolymer of natural rubber and poly(methyl methacrylate) (NR‐g‐PMMA) was prepared using semi‐batch emulsion polymerization technique via bipolar redox initiation system. It was found that the grafted PMMA increased with the increase of methyl methacrylate (MMA) concentration used in the graft copolymerization. The NR‐g‐PMMA was later used to prepare thermoplastic vulcanizates (TPVs) by blending with PMMA through dynamic vulcanization technique. Conventional vulcanization (CV) and efficient sulphur vulcanization (EV) systems were studied. It was found that the CV system provided polymer melt with lower shear stress and viscosity at a given shear rate. This causes ease of processability of the TPVs via extrusion and injection molding processes. Furthermore, the TPVs with the CV system showed higher ultimate tensile strength and elongation. The results correspond to the morphological properties of the TPVs. That is, finer dispersion of the small vulcanized rubber particles were observed in the PMMA matrix. Various blend ratios of the NR‐g‐PMMA/PMMA blends using various types of NR‐g‐PMMA (i.e. prepared using various percentage molar ratios of NR and MMA) were later studied via dynamic vulcanization by a conventional sulphur vulcanization system. It was found that increasing the level of PMMA caused increasing trend of the tensile strength and hardness properties but decreasing level of elongation properties. Increasing level of the grafted PMMA in NR molecules showed the same trend of mechanical properties as in the case of increasing concentration of PMMA used as a blend component. From morphological studies, two phase morphologies were observed with a continuous PMMA phase and dispersed elastomeric phase. It was also found that more finely dispersed elastomeric phase was obtained with increasing the grafted PMMA in the NR molecules. Copyright © 2005 John Wiley & Sons, Ltd.     

Tensile properties of ultradrawn polyethylene

High-density polyethylene filaments prepared by a solid-state deformation in an Instron capillary rheometer show unusually high crystal orientation, chain extension, axial modulus, and ultimate tensile strength. The Young's modulus and ultimate tensile strength have been determined from stress–strain curves. Gripping of this high modulus polyethylene has been a problem heretofore, but the measurement of ultimate tensile strength has now been made feasible by a special gripping procedure. Tensile moduli show an increase with sample preparation temperature and pressure. Values as high as 6.7 × 10¹¹ dyne/cm² are obtained from samples extruded at 134°C and 2400 atm and tested at a strain rate of 3.3 × 10^?4 sec^?1. The effect of strain rate and frequency on modulus has also been evaluated by a combination of stress–strain data and dynamic tension plus sonic measurements over nine decades of time.     

Effects of humidity on Young's modulus in poly(methyl methacrylate)

Tensile tests on poly (methyl methacrylate) (PMMA) were conducted to clarify the effects of humidity and strain rate on tensile properties, particularly Young's modulus. Prior to the tensile tests, specimens were kept under various humidity conditions at 293 K, which were the same as the test conditions, for a few months to adjust the sorbed water content in the specimens. The tensile tests were performed under each humidity condition at three different strain rates (approximately 1.4 × 10^?3, 1.4 × 10^?4, and 1.4 × 10^?5 s^?1). Stress‐strain curves changed with humidity and strain rate. Young's moduli were also measured at small applied stresses (below 6.7 MPa) under various humidity conditions at 293 K. Young's modulus decreases linearly with increasing humidity and a decreasing logarithm of strain rate. These results suggest that Young's modulus of PMMA can be expressed as a function of two independent parameters that are humidity and strain rate. A constitutive equation for Young's modulus of PMMA was proposed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 460–465, 2002; DOI 10.1002/polb.10107     

Occurrence of rippling during the deformation of oriented polyethylene

Rippling is another mode, in addition to kink-band formation, by which oriented polyethylene can deform and results in a profuse and irregular waviness in the fibrils. For the medium-density and high-density polyethylenes investigated, rippling tended to occur only at strain rates below about 1 min^?1 at 25°C. Above this rate, kink bands tended to form. It is suggested that rippling results from easy slip between the fibrils of the oriented polymers and from the resistance of the fibrils to shortening under a compressive stress. The applied shear stress is reduced by the easy slip to a simple compression along the fibrils, and this distorts the fibril into the series of waves that constitutes rippling. Stress–strain measurements confirm that fibril slip is considerably easier under the rates at which rippling occurs than at the rates at which kink bands form.     

The influence of sub-Tg annealing on environmental stress cracking resistance of polycarbonate

To explore the effect of physical aging on environmental stress cracking (ESC) behavior of polycarbonate (PC), sub-T_g annealing was utilized as a method for accelerated aging. Injection molded samples were annealed at 130 °C for different time varying up to 96 h. A three point bending apparatus was used to evaluate critical stress for crazing and to record the variation of stress with immersion time at constant strain. The ESC results indicated that the critical stress for crazing initiation of PC in ethanol is increased by sub-T_g annealing. However, the resistance of annealed PC to ESC with immersion time during the stress relaxation test depends on the level of initial stress. When a relatively low initial stress was used, a short time (24 h) of sub-T_g annealing reduced the stress relaxation rate and decreased the number of cracks on the surface of PC. However, under higher initial stress, the stress relaxation rate of PC had a slight change only when the annealing time was prolonged about threefold (72 h). This can be explained by the formation of cohesional entanglement sites during the sub-T_g annealing process, which was demonstrated by the thermal and dynamic mechanical tests.